# FPRAS for the Potts Model and the Number of $k$-colorings

## TL;DR

This paper introduces a Fully Polynomial Randomized Approximation Scheme (FPRAS) for efficiently approximating the partition function of the Potts model and counting the number of k-colorings in graphs, using Markov chain sampling.

## Contribution

It presents the first FPRAS for the Potts model and graph k-coloring counting problems based on a novel Markov chain sampling algorithm.

## Key findings

- Developed an efficient sampling algorithm for the Potts model
- Provided FPRAS for the Potts model partition function
- Provided FPRAS for counting k-colorings

## Abstract

In this paper, we give a sampling algorithm for the Potts model using Markov chains. Based on the sampling algorithm, we give \emph{FPRAS}es for the Potts model and the number of $k$-colorings of the graph.

---
Source: https://tomesphere.com/paper/1902.09114